With just over a week to go before the start of the climate conference in Glasgow, public safety minister Ash Regan wrote to Ken Dalling, president of the Law Society of Scotland, and Julia McPartlin, president of the Scottish Solicitors Bar Association, addressing the plan.
The three principal bar associations in Scotland - in Glasgow, Edinburgh and Aberdeen - have all said they will not take part while associations in Alloa, Falkirk and Hamilton will also boycott.
Plans were unveiled earlier this year to allow for weekend sittings of courts in Glasgow along with Saturday sittings in Edinburgh and Aberdeen during the conference.
However, the profession says it is already underfunded and understaffed.
Extra funding was proposed by the Scottish Government to compensate lawyers for the scheme but the bar associations decided to boycott.
"The Scottish Legal Aid Board (SLAB) and Scottish Government have engaged with the representatives of the legal profession in good faith over the past few months to agree an enhanced package of legal aid fees to ensure that access to necessary legal representation would be available during the period of the Cop26 conference," the minister said in her letter.
"Scottish ministers have agreed the specific proposals and requests from the representatives of the profession.
"We are, therefore, surprised and disappointed by the decision of individual bar associations not to participate in the Cop26 duty scheme on the basis of the enhanced fee package approved in line with the Law Society of Scotland's own proposals."
Ms Regan goes on to say a "further immediate, permanent and substantial increase to all legal aid fees - additional to the specific enhanced fees already agreed - to allay concerns that legal practitioners have in participating during the Cop26 conference is not something that any government could agree to".
Legal aid fees increased by 5% this year and are due to go up by the same amount next year.”
In a letter to Ms Regan, Justice Secretary Keith Brown and SLAB chief executive Colin Lancaster, Glasgow Bar Association president Fiona McKinnon said: "As an association, we are seeking immediate discussions with you and our colleagues in the affected bar associations, Law Society of Scotland representatives and our Scottish Solicitors Bar Association (SSBA) colleagues.
"We are seeking a commitment to a substantial increase in the legal aid rates and not simply the 5% promised by regulations next March, pending long-awaited legal aid reform and a mechanism to review future legal aid provision to reflect the commitment of practitioners to this essential work for the most vulnerable members of our society."
Defence lawyers have also been locked in a dispute with the Scottish Government for almost a year over having to work public holidays.
The letter added: "We are also seeking a commitment to resolve the holiday court dispute before the next national holiday, which is St Andrew's Day, a year after our association started action to address this matter.
"Only once we have a commitment from you about these essential matters would we be willing to make a recommendation to our members to consider participating in the Cop26 duty plan and weekend courts for own clients."